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Dissertations / Theses on the topic 'Riemann hypothesis'

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Published: 4 June 2021

Last updated: 25 July 2025

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1

Aronsson, Carl, and Gösta Kamp. "The Riemann Hypothesis." Thesis, KTH, Matematik (Inst.), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127725.

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The Riemann hypothesis was first proposed by Bernhard Riemann in 1860 [1] and says all non-trivial zeroes to the Riemann zeta function lie on the line with the real part 12 in the complex plane [1]. If proven to be true this would give a much better approximation of the number of prime numbers less than some number X. The Riemann hypothesis is regarded to be one of the most important unsolved mathematical problems. It is one of the Clay InstituteMilleniumproblems and originally one of the unsolved problems presented by David Hilbert as essential for 20th century mathematics at International C

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2

Henderson, Cory. "Exploring the Riemann Hypothesis." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1371747196.

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3

Juchmes, Franziska. "Zeta Functions and Riemann Hypothesis." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-32363.

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In this thesis the zeta functions in analytic number theory are stud-ied. The distribution of primes and the connection between primes andzeta functions are discussed. Numerical results for linear combinationsof zeta functions are presented. These functions have a symmetric dis-tribution of zeros around the critical line.

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4

Bielik, Alexander. "An introduction to the Riemann hypothesis." Thesis, KTH, Matematik (Inst.), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-153636.

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This paper exhibits the intertwinement between the prime numbers and the zeros of the Riemann zeta function, drawing upon existing literature by Davenport, Ahlfors, et al. We begin with the meromorphic continuation of the Riemann zeta function ζ and the gamma function Γ . We then derive a functional equation that relates these functions and formulate the Riemann hypothesis. We move on to the topic of nite-ordered functions and their Hadamard products. We show that the xi function ξ is of finite order, whence we obtain many useful properties. We then use these properties to and a zero-free regi

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5

Nawaz, Daud. "The Dirichlet Series To The Riemann Hypothesis." Thesis, Högskolan i Gävle, Avdelningen för elektronik, matematik och naturvetenskap, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-27028.

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This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. This paper explains that the non-trivial zeros of the zeta-function are the key to understand the prime distribution.

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6

Tarkhanov, Nikolai. "A simple numerical approach to the Riemann hypothesis." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5764/.

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The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.

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7

Bradford, Alexander. "Automated Conjecturing Approach to the Discrete Riemann Hypothesis." VCU Scholars Compass, 2016. http://scholarscompass.vcu.edu/etd/4470.

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This paper is a study on some upper bounds of the Mertens function, which is often considered somewhat of a ``mysterious" function in mathematics and is closely related to the Riemann Hypothesis. We discuss some known bounds of the Mertens function, and also seek new bounds with the help of an automated conjecture-making program named CONJECTURING, which was created by C. Larson and N. Van Cleemput, and inspired by Fajtowicz's Dalmatian Heuristic. By utilizing this powerful program, we were able to form, validate, and disprove hypotheses regarding the Mertens function and how it is bounded.

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8

Alcántara, Bode Julio. "A conjecture about the non-trivial zeroes of the Riemann zeta function." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/97185.

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Some heuristic arguments are given in support of the following conjecture: If the Riemann Hypothesis (RH) does not hold then the number of zeroes of the Riemann zeta function with real part σ > ½ is infinite.

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9

Ranorovelonalohotsy, Marie Brilland Yann. "Riemann hypothesis for the zeta function of a function field over a finite field." Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85713.

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10

Lucas, Fábio Rodrigues. "Polinômios e funções inteiras com zeros reais." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306953.

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Orientador: Dimitar Kolev Dimitrov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-16T01:35:19Z (GMT). No. of bitstreams: 1 Lucas_FabioRodrigues_D.pdf: 837192 bytes, checksum: 1cec40a06f620203e95cbca6134fd41a (MD5) Previous issue date: 2010<br>Resumo: Nesta tese abordamos alguns problemas relacionados com zeros de polinômios e de funções inteiras. Estabelecemos fórmulas explícitas para os polinômios da sequência de Sturm, gerada por um polinômio e pela sua derivada. Como consequência,

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11

Alvites, José Carlos Valencia. "Hipótese de Riemann e física." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13042012-084309/.

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Neste trabalho, introduzimos a função zeta de Riemann \'ZETA\'(s), para s \'PERTENCE\' C \\ e apresentamos muito do que é conhecido como justificativa para a hipótese de Riemann. A importância de \'ZETA\' (s) para a teoria analítica dos números é enfatizada e fornecemos uma prova conhecida do Teorema dos Números Primos. No final, discutimos a importância de \'ZETA\'(s) para alguns modelos físicos de interesse e concluimos descrevendo como a hipótese de Riemann pode ser acessada estudando estes sistemas<br>In this work, we introduce the Riemann zeta function \'ZETA\'(s), s \'IT BELONGS\' C \\

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12

Zhao, Lin. "Spherical and Spheroidal Harmonics: Examples and Computations." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1512004235488354.

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13

Gulas, Michael Allen. "Using Hilbert Space Theory and Quantum Mechanics to Examine the Zeros of The Riemann-Zeta Function." Bowling Green State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1594035551136634.

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14

Velasquez, Castanon Oswaldo. "Sur la répartition des zéros de certaines fonctions méromorphes liées à la fonction zêta de Riemann." Thesis, Bordeaux 1, 2008. http://www.theses.fr/2008BOR13622/document.

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Nous traitons trois problèmes liés à la fonction zêta de Riemann : 1) L'établissement de conditions pour déterminer l'alignement et la simplicité de la quasi-totalité des zéros d'une fonction de la forme f(s)=h(s)±h(2c-s), où h(s) est une fonction méromorphe et c un nombre réel. Cela passe par la généralisation du théorème d'Hermite-Biehler sur la stabilité des fonctions entières. Comme application, nous avons obtenu des résultats sur la répartition des zéros des translatées de la fonction zêta de Riemann et de fonctions L, ainsi que sur certaines intégrales de séries d'Eisenstein. 2) L'étude

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15

Schlackow, Waldemar. "A sieve problem over the Gaussian integers." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:b7d4ff88-1f93-41b4-9f81-055f8f1b1c51.

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Our main result is that there are infinitely many primes of the form a² + b² such that a² + 4b² has at most 5 prime factors. We prove this by first developing the theory of $L$-functions for Gaussian primes by using standard methods. We then give an exposition of the Siegel--Walfisz Theorem for Gaussian primes and a corresponding Prime Number Theorem for Gaussian Arithmetic Progressions. Finally, we prove the main result by using the developed theory together with Sieve Theory and specifically a weighted linear sieve result to bound the number of prime factors of a² + 4b². For the application

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16

Coatney, Ryan D. "Mean Square Estimate for Primitive Lattice Points in Convex Planar Domains." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2501.

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The Gauss circle problem in classical number theory concerns the estimation of N(x) = { (m1;m2) in ZxZ : m1^2 + m2^2 <= x }, the number of integer lattice points inside a circle of radius sqrt(x). Gauss showed that P(x) = N(x)- pi * x satisfi es P(x) = O(sqrt(x)). Later Hardy and Landau independently proved that P(x) = Omega_(x1=4(log x)1=4). It is conjectured that inf{e in R : P(x) = O(x^e )}= 1/4. I. K atai showed that the integral from 0 to X of |P(x)|^2 dx = X^(3/2) + O(X(logX)^2). Similar results to those of the circle have been obtained for regions D in R^2 which contain the origin and w

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17

Powell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.

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The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely

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18

Nazardonyavi, Sadegh. "A class of Equivalent Problems Related to the Riemann Hypothesis." Doctoral thesis, 2013. https://repositorio-aberto.up.pt/handle/10216/68968.

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19

Nazardonyavi, Sadegh. "A class of Equivalent Problems Related to the Riemann Hypothesis." Tese, 2013. https://repositorio-aberto.up.pt/handle/10216/68968.

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20

Droll, ANDREW. "Variations of Li's criterion for an extension of the Selberg class." Thesis, 2012. http://hdl.handle.net/1974/7352.

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In 1997, Xian-Jin Li gave an equivalence to the classical Riemann hypothesis, now referred to as Li's criterion, in terms of the non-negativity of a particular infinite sequence of real numbers. We formulate the analogue of Li's criterion as an equivalence for the generalized quasi-Riemann hypothesis for functions in an extension of the Selberg class, and give arithmetic formulae for the corresponding Li coefficients in terms of parameters of the function in question. Moreover, we give explicit non-negative bounds for certain sums of special values of polygamma functions, involved in the arith

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21

Gupta, Nikhil. "On symmetries of and equivalence tests for two polynomial families and a circuit class." Thesis, 2022. https://etd.iisc.ac.in/handle/2005/5843.

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Two polynomials f, g ∈ F[x1, . . . , xn] over a field F are said to be equivalent if there exists an n×n invertible matrix A over F such that g = f(Ax), where x = (x1 · · · xn)T . The equivalence test (in short, ET) for a polynomial family {fm}m∈N (similarly, a circuit class C ) is the following algorithmic problem: Given input black-box access to g ∈ F[x1, . . . , xn], determine whether there exists an f ∈ {fm}m∈N (respectively, a circuit C ∈ C ) such that g = f(Ax) (respectively, g = C(Ax)) for some n × n invertible matrix A over F. If the answer is yes, it also outputs an f ∈ {fm}m∈N

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